$f(t) = -2t^{2}-6t-2(h(t))$ $h(n) = 4n^{2}-4n-4$ $g(t) = -7t^{2}+t+5(f(t))$ $ h(f(-1)) = {?} $
Solution: First, let's solve for the value of the inner function, $f(-1)$ . Then we'll know what to plug into the outer function. $f(-1) = -2(-1)^{2}+(-6)(-1)-2(h(-1))$ To solve for the value of $f$ , we need to solve for the value of $h(-1)$ $h(-1) = 4(-1)^{2}+(-4)(-1)-4$ $h(-1) = 4$ That means $f(-1) = -2(-1)^{2}+(-6)(-1)+(-2)(4)$ $f(-1) = -4$ Now we know that $f(-1) = -4$ . Let's solve for $h(f(-1))$ , which is $h(-4)$ $h(-4) = 4(-4)^{2}+(-4)(-4)-4$ $h(-4) = 76$